In the given transaction, the output that was sent to the same address was the change. I know the story about change.
but I am asking is it possible to sent from address "A" to address "A" without any other output addresses ?
Yes. A transaction simply takes in inputs and spits out outputs, it doesn't care what the addresses are, so long as the input script properly spends the output script of the output it spends.
Excatly, it doesn't matter if it's change or not.
It's not like there's a special design for change anyways.